Notation - Odd and Even Cases in one

Question

Consider the function $$\begin{cases} \displaystyle\sum_{r=0}^{2\mu}f(r)(-1)^r\qquad \text{for even $\mu$}\\ \displaystyle\sum_{r=0}^{2\mu}f(r)(-1)^{r+1}\qquad \text{for odd $\mu$}\\\end{cases}$$

Is there a neat notation where the two expressions can be combined into one which will automatically cater for both even and odd values of $\mu$ without splitting into two cases?

@ThomasAndrews - Thanks. That works perfectly. Would you like to post this as an answer? I was thinking of using the indicator function but that's probably too cumbersome. — Hypergeometricx, Nov 25 '16 at 16:36

score 2 · Answer 1 · answered Nov 25 '16 at 16:34

2

$$\sum_{r=0}^{2\mu}f(r)(-1)^{r+\mu}$$

answered Nov 25 '16 at 16:34

Thanks. That works very well. As mentioned in the comment above, I was thinking of using the indicator function but that's probably too cumbersome. – Hypergeometricx Nov 25 '16 at 16:38

Notation - Odd and Even Cases in one

1 Answers1